How high can a roller coaster be? a roller coaster car is to roll down a frictionless ramp into a loop of a radius r. if the riders can withstand an acceleration of 9g's and not black out - i. e. their apparent weight at the bottom of the loop is nine times their actual weight; what is the maximum height of the incline if the cars starts from the rest?

h=4r

Explanation:

To solve the problem it is necessary to apply the energy conservation equations for the roller coaster.

The energy conservation equations warn that:

Where,

Kinetic Energy

Potential Energy

Equating,

Re-arrange for V,

For balance of forces, according to the announcement, those who are on a roller coaster can withstand up to a maximum of 9g.

Therefore, considering the centripede speed and the speed of the fall, we obtain that,

The centripetal acceleration is given by the equation

Where

V = Tangencial velocity

r = Radius

Then replacing in the equation of Force,

Therefore the maximum height of the incline if the cars starts from the rest is 4 times the raidus of the inclination